We introduce a nonconforming virtual element method for the Poisson equation on domains with curved boundary and internal interfaces. We prove arbitrary order optimal convergence in the energy and $L^2$ norms, and validate the theoretical results with numerical experiments. Compared to existing nodal virtual elements on curved domains, the proposed scheme has the advantage that it can be designed in any dimension.

翻译：本文针对具有曲边界和内界面的区域上的泊松方程，提出了一种非协调虚拟元方法。我们证明了该方法在能量范数和$L^2$范数下的任意阶最优收敛性，并通过数值实验验证了理论结果。与现有针对曲区域的节点虚拟元方法相比，所提方案的优势在于可在任意维度上进行设计。